Optimal. Leaf size=67 \[ -\frac {a^5}{12 x^{12}}-\frac {5 a^4 b}{11 x^{11}}-\frac {a^3 b^2}{x^{10}}-\frac {10 a^2 b^3}{9 x^9}-\frac {5 a b^4}{8 x^8}-\frac {b^5}{7 x^7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ -\frac {a^3 b^2}{x^{10}}-\frac {10 a^2 b^3}{9 x^9}-\frac {5 a^4 b}{11 x^{11}}-\frac {a^5}{12 x^{12}}-\frac {5 a b^4}{8 x^8}-\frac {b^5}{7 x^7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x^{13}} \, dx &=\int \left (\frac {a^5}{x^{13}}+\frac {5 a^4 b}{x^{12}}+\frac {10 a^3 b^2}{x^{11}}+\frac {10 a^2 b^3}{x^{10}}+\frac {5 a b^4}{x^9}+\frac {b^5}{x^8}\right ) \, dx\\ &=-\frac {a^5}{12 x^{12}}-\frac {5 a^4 b}{11 x^{11}}-\frac {a^3 b^2}{x^{10}}-\frac {10 a^2 b^3}{9 x^9}-\frac {5 a b^4}{8 x^8}-\frac {b^5}{7 x^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 67, normalized size = 1.00 \[ -\frac {a^5}{12 x^{12}}-\frac {5 a^4 b}{11 x^{11}}-\frac {a^3 b^2}{x^{10}}-\frac {10 a^2 b^3}{9 x^9}-\frac {5 a b^4}{8 x^8}-\frac {b^5}{7 x^7} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.44, size = 57, normalized size = 0.85 \[ -\frac {792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.23, size = 57, normalized size = 0.85 \[ -\frac {792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 58, normalized size = 0.87 \[ -\frac {b^{5}}{7 x^{7}}-\frac {5 a \,b^{4}}{8 x^{8}}-\frac {10 a^{2} b^{3}}{9 x^{9}}-\frac {a^{3} b^{2}}{x^{10}}-\frac {5 a^{4} b}{11 x^{11}}-\frac {a^{5}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.36, size = 57, normalized size = 0.85 \[ -\frac {792 \, b^{5} x^{5} + 3465 \, a b^{4} x^{4} + 6160 \, a^{2} b^{3} x^{3} + 5544 \, a^{3} b^{2} x^{2} + 2520 \, a^{4} b x + 462 \, a^{5}}{5544 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 56, normalized size = 0.84 \[ -\frac {\frac {a^5}{12}+\frac {5\,a^4\,b\,x}{11}+a^3\,b^2\,x^2+\frac {10\,a^2\,b^3\,x^3}{9}+\frac {5\,a\,b^4\,x^4}{8}+\frac {b^5\,x^5}{7}}{x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.62, size = 61, normalized size = 0.91 \[ \frac {- 462 a^{5} - 2520 a^{4} b x - 5544 a^{3} b^{2} x^{2} - 6160 a^{2} b^{3} x^{3} - 3465 a b^{4} x^{4} - 792 b^{5} x^{5}}{5544 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________